Phase-field model of mode III dynamic fracture.

By Alain Karma, David A. Kessler, Herbert Levine. Physical Review Letters, 2001

626 citations recorded by the source corpus.

We introduce a phenomenological continuum model for the mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between "broken" and "unbroken" states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short-scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.

Subfields: Computational Mechanics, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/14a1a2bded6ce8fb934388d227846e54eb4988d7

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In Computational Mechanics

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Why do cracks branch? A peridynamic investigation of dynamic brittle fracture (2015, methodology): “Two approaches have been favored in this area: dynamic phase-field fracture models based on Landau–Ginzburg type phase-field evolution equations (e.g., Karma et al. 2001; Spatschek et al. 2011) and phase-field formulations based onGriffith’s theory (see Bourdin et al. 2008, 2011).”
Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation (2012, methodology): “Conceptually similar are phase field approaches to brittle fracture based on the classical Ginzburg–Landau type evolution equation as reviewed in Hakim and Karma (2009), see also Karma et al. (2001) and Eastgate et al. (2002).”
Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations (2010, methodology): “Conceptually similar are recently outlined phase field approaches to brittle fracture based on the classical Ginzburg–Landau type evolution equation as reviewed in Hakim & Karma [20], see also Karma, Kessler & Levine [23] and Eastgate et al.”
Phase-field modeling of hydraulic fracture (2016, background): “Examples of diffuse crack approaches include peridynamics([37,38]), gradient damage mechanics([39,40]), and the phase-field methods presented herein and by other recent studies([41-53]).”
Phase-field modeling of anisotropic brittle fracture including several damage mechanisms (2018, neutral): “They share a conceptual resemblance with Ginzburg-Landau formulations [2, 3] of phase transitions and can also be interpreted as damage gradient models [4, 5] in which the dissipated energy density contains a regularizing damage gradient term associated with a regularizing internal length scale.”
Phase field modelling of anisotropic crack propagation (2017, neutral): “Alternatively the quartic function, and the cubic function are introduced in the work of Karma et al. (2001), Borden (2012).”
Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms (2017, methodology): “Inclusion of a viscous dissipation energy, as initially introduced in [33] and proposed in [45] as a purely artificial regularization to improve numerical stability, would enable to introduce a rate-dependent effect reducing the value of the computed velocities.”
Laws of crack motion and phase-field models of fracture (2008, methodology): “Our conclusions and some further perspectives of this work are then presented in Section 8. Further information on the phase-field model of Karma et al. (2001) is provided in Appendix A in the simple context of a stretched one-dimensional band.”
Crack nucleation in variational phase-field models of brittle fracture (2018, positive): “They are nowadays known as phase-ﬁeld models of fracture, and share several common points with the approaches coming from Ginzburg-Landau models for phase-transition [57].”